Electromotive Force

Question 1

Electromotive Force

1. In a circuit, electromotive force is the energy per unit charge converted from the other forms of energy into electrical energy to move the charge across the whole circuit.
   In equation,
   

where
E = e.m.f.,
W = energy converted from non-electrical forms to electrical form
Q = positive charge.

1. The unit of e.m.f. is JC^-1 or V (Volt)
2. The unit of e.m.f. is JC^-1 or V (Volt). Electromotive force of 1 Volt means that 1 Joule of electrical energy is supplied to the circuit to move 1 Coulomd of charge across the whole circuit.

Question 2

Difference between Electromotive Force and Potential Difference

Electromotive Force and Potential Difference

Similarities:
Have same unit (Volt)
Can be measured by Voltmeter

Electromotive Force

Definition:
The electromotive force (e.m.f.) is defined as the energy per unit charge that is converted from chemical, mechanical, or other forms of energy into electrical energy in a battery or dynamo.

Symbol:
Denoted by the symbol, E

Potential Difference

Definition:
The potential difference (p.d.) between two points is defined as the energy converted from electrical to other forms when one coulomb of positive charge passes between the two points.

Symbol:
Denoted by the symbol, V

Question 3

Internal Resistance and Potential Difference Drop

Internal Resistance

The internal resistance of a source (cell or generator) is the resistance against the moving charge in the source.

Load Resistance

The load resistance in a circuit is the effective resistance against the moving charge outside the source of electric.

Terminal Potential Difference

Terminal potential difference or terminal voltage is the potential difference across the two terminal (the positive terminal and the negative terminal) of an electric source (cell or generator).

Question 4

Internal Resistance and Potential Difference Drop

1. If the internal resistance is ignored, the terminal potential difference is equal to the e.m.f.
2. If the internal resistance is present, the terminal potential difference will be lower than the e.m.f.
3. The relationship between e.m.f. and the terminal potential difference is given by the following equation.
   Equation
   

E = e.m.f.
V = terminal potential difference
I = current flows in the circuit
r = internal resistance
R = the load resistance

Question 5

A cell has internal resistance 0.5Ω and the potential difference across the cell is 4V when a 2A current flows through it. Find the e.m.f. of the cell.

Answer 5

r = 0.5Ω
V = 4V
I = 2A
E = ?

Question 6

A cell with e.m.f. 3V and internal resistance, 1Ω is connected to a 5Ω resistor, and a voltmeter is connected across the resistor as shown in the diagram on the left. Find the reading of the voltmeter.

Answer 6

E = 3V
r = 1Ω
R = 5Ω
V = ?

Question 7

Measuring e.m.f. and Internal Resistance

Three methods can be used to measure the e.m.f. and internal resistance.

1. Open circuit - Closed circuit
2. Simultaneous Equation
3. Linear Graph

Question 8

Measuring e.m.f. and Internal Resistance - Open Circuit/Close Circuit

Open Circuit Close Circuit

In open circuit (when the switch is off), the voltmeter shows the reading of the e.m.f.

In closed circuit (when the switch is on), the voltmeter shows the reading of the potential difference across the cell. With the presence of internal resistance, the potential difference across the cell is always less than the e.m.f.

Question 9

The diagram above shows a simple circuit that connect some baterries to a resistor. The voltmeter shows a reading of 3.0V when the switch is off and 2.4V when the switch is on. What are the e.m.f. and the internal resistance of the cell?

Answer 9

When the switch is off, the reading of the voltmeter shows the e.m.f. of the batteries. Therefore.
e.m.f. = 3.0V

When the switch in turned on, the reading of the voltmeter shows the potential difference of the resistor. Therefore,
V = 2.4V

The current that passes through the resistor and the internal resistance of the battery,

Question 10

Diagram (a)

Diagram (b)

A cell is connected to a circuit as shown in diagram (a). The graph in diagram (b) shows the change of the reading of the voltmeter, V against time, t. If t is the time where the switch is close, find

(a) the e.m.f. of the cell
(b) the internal resistance of the cell.

Answer 10

(a) Before the switch turned on, the reading of the ammeter shows the e.m.f. of the cells.

From the graph, the e.m.f. = 3.0V

(b)
e.m.f., E = 3.0V
Potential difference across the resistor, V = 2.5V

Current that pass through the resistor,

Question 11

When a 1Ω resistor is connected to the terminal of a cell, the current that flows through it is 8A. When the resistor is replaced by another resistor with resistance 4Ω, the current becomes 2⅔A.

Find the:

a. internal resistance of the cell
b. e.m.f. of the cell

Answer 11

Experiment 1
R₁ = 1Ω
I₁ = 8A

Experiment 2
R₂ = 4Ω
I₂ = 2⅔A

Solve the simultaneous equation
E = 12V, r = 0.5Ω

Question 12

The diagram on the left shows that the terminal potential difference of a batteries is 1.2V when a 4 Ω resistor is connected to it. The terminal potential become 1.45V when the resistor is replaced by another resistor of resistance 29Ω

Find the

a. internal resistance, r
b. e.m.f. of the batteries.

Answer 12

Answer:
Experiment 1
V₁ = 1.2V
R₁ = 4Ω

Experiment 2
V₂ = 1.45V
R₂ = 29

Solve the simultaneous equation
E = 1.5V, r = 1Ω

Question 13

The Linear Graph

From the equation,

Y axis = Potential difference (V)
X axis = Current (I)
Gradient of the grapf, m = - internal resistance (r)
Y intercept of the graph, c = e.m.f.

Question 14

The graph shows the variation of potential difference with current of a battery.
What is the internal resistance and e.m.f. of the battery?

Answer 14

• *Answer**:
  e. m.f. = y-intercept = 3V

internal resistance,
r = -gradient of the graph